Velocity multistability vs ergodicity breaking in a biased periodic potential

TL;DR

This paper investigates how velocity multistability and ergodicity breaking manifest in a Brownian particle moving in a biased periodic potential, highlighting the effects of temperature and initial conditions on system dynamics.

Contribution

It provides a detailed analysis of velocity multistability and ergodicity breaking in a driven Brownian particle, emphasizing the influence of temperature and initial conditions.

Findings

Velocity multistability depends on initial conditions at low temperatures.

Ergodicity is restored at higher temperatures, reducing initial condition dependence.

Multistability remains robust at moderate and high temperatures.

Abstract

Multistability, i.e. the coexistence of several attractors for a given set of system parameters is one of the most important phenomena occurring in dynamical systems. We consider it in velocity dynamics of a Brownian particle driven by thermal fluctuations and moving in a biased periodic potential. In doing so we focus on the impact of ergodicity - a concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and as a consequence the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperature the ergodicity is in principle restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperature the multistability is robust with respect to the choice of the starting position and velocity of the particle.